Introduction to Digital Signal Processing

by Karl, John H.

• ISBN13: 9780123984203
• ISBN10: 0123984203
• Format: Hardcover
• Copyright: 1989-07-01
• Publisher: Academic Pr

Summary

An Introduction to Digital Signal Processing is written for those who need to understand and use digital signal processing and yet do not wish to wade through a multi-semester course sequence. Using only calculus-level mathematics, this book progresses rapidly through the fundamentals to advanced topics such as iterative least squares design of IIR filters, inverse filters, power spectral estimation, and multidimensional applications--all in one concise volume. This book emphasizes both the fundamental principles and their modern computer implementation. It presents and demonstrates how simple the actual computer code is for advanced modern algorithms used in DSP. Results of these programs, which the reader can readily duplicate and use on a PC, are presented in many actual computer drawn plots. Key Features * assumes no previous knowledge of signal processing but leads up to very advanced techniques combines exposition of fundamental principles with practical applications * includes problems with each chapter * presents in detail the appropriate computer algorithums for solving problems

Table of Contents

Preface	xi
Signals and Systems
Sampling and Aliasing	4	(4)
Linear Time-Invariant Systems and the Convolution Operation	8	(10)
Constant-Coefficient Difference Equations	18	(3)
System Block Diagrams and Flow Graphs	21	(3)
Problems	24	(3)
Sampled Data and the Z Transform
The Z Transform, Polynomial Multiplication, and Convolution	27	(2)
Factoring Z Transforms into Couplets	29	(1)
Inverse Operators: Stability, Causality, and Minimum Phase	30	(7)
Problems	37	(5)
Sinusoidal Response of LSI Systems
Sinusoidal Signals as Eigenfunctions and the Spectrum as Eigenvalues	42	(2)
Frequency Response of Some Simple LSI Systems	44	(6)
Frequency Response of Digital Differential and Integral Operators	50	(3)
The Bilinear Transform and Its Application to Differential Equations	53	(7)
Problems	60	(5)
Couplets and Elementary Filters
The Single-Zero Couplet	65	(4)
The Single-Pole Couplet	69	(2)
The Single-Zero, Single-Pole, Allpass Filter	71	(3)
Elementary Filters Classified by Their Poles and Zeros	74	(2)
Problems	76	(3)
The Discrete Fourier Transform
Sampling the System Response in the Frequency Domain	79	(3)
Properties of the DFT	82	(4)
Special Values of the DFT	86	(1)
The Phase-Shift Theorem	87	(1)
The Convolution Theorem	88	(3)
Cross-Correlation and Autocorrelation	91	(2)
Problems	93	(5)
The Continuous Fourier Integral Transform
The Fourier Integral Transform Developed from the DFT	98	(4)
Properties of the Fourier Integral Transform	102	(2)
The Wiener--Khintchine Theorem	104	(2)
The Time-Limited Band-Limited Theorem	106	(1)
A Repertoire of Transforms and Their Importance	107	(17)
Problems	124	(4)
Application of the Fourier Transform to Digital Signal Processing
Continuous Time, Discrete Frequency: The Fourier Series	128	(3)
The Least-Squares Convergence of the Fourier Series	131	(2)
The Sampling Function	133	(2)
The Relationship between the FT and the DFT: Resolution and Leakage	135	(8)
Interpolation, Decimation, and Multiplexing	143	(6)
Digital Control Systems	149	(11)
Problems	160	(7)
Digital Filter Design
Digital Filter Design---The Problem	167	(4)
Designing FIR Filters Using Windows	171	(4)
Frequency Sampling and the Parks--McClellan Algorithm	175	(7)
Recursive Filters	182	(3)
Digitizing Rational Functions of ω	185	(5)
DFT Frequency Filtering	190	(2)
Problems	192	(6)
Inverse Filtering and Deconvolution
Exact Inverses via the DFT	198	(5)
Linear Deconvolution---The Problem	203	(3)
Winear Least-Squares Filters	206	(2)
Application to Inverses	208	(3)
Filter Delay Properties	211	(2)
Applications to Prediction Filters	213	(4)
Matched Filters and Output Energy Filters	217	(8)
The Levinson Recursion	225	(3)
Appendix: The Least-Squares Property of Wiener Filters	228	(2)
Problems	230	(6)
Spectral Factorization
The Root Method	236	(2)
The Spectrum of a Real Causal Function	238	(4)
Kolmogoroff Factorization	242	(3)
Least-Squares Zero-Delay Factorization	245	(1)
Iterative Least-Squares Factorization	246	(4)
Applications to IIR Filter Design	250	(3)
Problems	253	(8)
Power Spectral Estimation
Signal-Like and Noise-Like Processes---The PSD Problem	261	(6)
The MA Model: The Approach of Blackman and Tukey	267	(4)
The AR Model: The Approach of Yule--Walker and Burg	271	(8)
The Maximum Entropy Principle	279	(5)
Other Data Models	284	(3)
Problems	287	(7)
Multidimensional DSP
Multidimensional Difference Equations	294	(16)
Fourier Transform Methods in Multidimensions	310	(10)
Two-Dimensional FIR Frequency Filter Design	320	(6)
Problems	326	(7)
References	333	(2)
Index	335